anonymous
  • anonymous
how do you solve 16^(-3/4) without a calculator?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
split the powers and then do individually
anonymous
  • anonymous
what do you mean by split the powers?
anonymous
  • anonymous
do u got it

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anonymous
  • anonymous
no, im lost where -3 is multiplyed by 6 and then the ^1/4 part
anonymous
  • anonymous
ok i explain in steps
theEric
  • theEric
(-3) means \[\frac{1}{16^3}\] and (1/4) means \[\sqrt[4]{16}\] right? So, since you're doing both to the 16... it can be written as \[\frac{1}{\sqrt[4]{16^3}}\] or \[\frac{1}{\sqrt[4]{16}^3}\]
anonymous
  • anonymous
that makes sense so far
theEric
  • theEric
Now, one looks much more easy to solve than the other, even though they are the same thing.
anonymous
  • anonymous
the power is -3/4 base is 16 now 16^-3 . 16^1/4=1/(16)^3.\[\sqrt[4]{16}\]
anonymous
  • anonymous
how does \[\sqrt[4]{16^3}\] turn into 8?
anonymous
  • anonymous
i know the answer is 1/8
anonymous
  • anonymous
\[\sqrt[4]{4096}\]
anonymous
  • anonymous
nvm
theEric
  • theEric
I would look at it the other way - just to avoid that huge number \[16^3\].
theEric
  • theEric
\[\frac{1}{\sqrt[4]{16}^3}\]
theEric
  • theEric
So it's like \[\frac{1}{(\sqrt[4]{16})^3}\]
theEric
  • theEric
And what is \[\sqrt[4]{16}\]?
theEric
  • theEric
Guess :P
theEric
  • theEric
It's a nice number.
anonymous
  • anonymous
2
anonymous
  • anonymous
sorry, i was afk for a while
anonymous
  • anonymous
then 2^3 is 8
anonymous
  • anonymous
so 1/8
anonymous
  • anonymous
thanks!
theEric
  • theEric
Understood! Thank you! And you're welcome!

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